Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
696 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16811582 | C2 | semidirect |
| 2. #20290442 | C2 | semidirect |
| 3. C2×#16811479 | C2 | semidirect |
| 4. #20289591 | C2 | semidirect |
| 35. #13133272 | D4 | semidirect |
| 191. C2×D53 | #329 | semidirect |
| 235. C53 | #9119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811582 | 2 |
| #20290442 | 2 |
| C2×#16811479 | 2 |
| #20289591 | 2 |
| #20283019 | 2 |
| #9119 | 53 |